There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper proposes a method of modeling and simulation of photovoltaic arrays. The main objective is to find the parameters of the nonlinear I-V equation by adjusting the curve at three points: open circuit, maximum power, and short circuit. Given these three points, which are provided by all commercial array data sheets, the method finds the best I-V equation for the single-diode photovoltaic (PV) model including the effect of the series and parallel resistances, and warranties that the maximum power of the model matches with the maximum power of the real array. With the parameters of the adjusted I-V equation, one can build a PV circuit model with any circuit simulator by using basic math blocks. The modeling method and the proposed circuit model are useful for power electronics designers who need a simple, fast, accurate, and easy-to-use modeling method for using in simulations of PV systems. In the first pages, the reader will find a tutorial on PV devices and will understand the parameters that compose the single-diode PV model. The modeling method is then introduced and presented in details. The model is validated with experimental data of commercial PV arrays.

Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays

The Smart Grid, regarded as the next generation power grid, uses two-way flows of electricity and information to create a widely distributed automated energy delivery network. In this article, we survey the literature till 2011 on the enabling technologies for the Smart Grid. We explore three major systems, namely the smart infrastructure system, the smart management system, and the smart protection system. We also propose possible future directions in each system. colorred{Specifically, for the smart infrastructure system, we explore the smart energy subsystem, the smart information subsystem, and the smart communication subsystem.} For the smart management system, we explore various management objectives, such as improving energy efficiency, profiling demand, maximizing utility, reducing cost, and controlling emission. We also explore various management methods to achieve these objectives. For the smart protection system, we explore various failure protection mechanisms which improve the reliability of the Smart Grid, and explore the security and privacy issues in the Smart Grid.

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Smart Grid — The New and Improved Power Grid: A Survey

Smart Grid - The New and Improved Power Grid:

Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the curse of dimensionality, heuristics-based swarm intelligence can be an efficient alternative. Particle swarm optimization (PSO), part of the swarm intelligence family, is known to effectively solve large-scale nonlinear optimization problems. This paper presents a detailed overview of the basic concepts of PSO and its variants. Also, it provides a comprehensive survey on the power system applications that have benefited from the powerful nature of PSO as an optimization technique. For each application, technical details that are required for applying PSO, such as its type, particle formulation (solution representation), and the most efficient fitness functions are also discussed.

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Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems

Preface. 1. Introduction. 1. Why Competition? 2. Dramatis Personae. 3. Models of Competition. 4. Open Questions. 5. Further Reading. 6. Problems. 2. Basic Concepts from Economics. 1. Introduction. 2. Fundamentals of Markets. 3. Concepts from the Theory of the Firm. 4. Types of Markets. 5. Markets with Imperfect Competition. 6. Further Reading. 7. Problems. 3. Markets for Electrical Energy. 1. Introduction. 2. What is the Difference between a Megawatt--hour and a Barrel of Oil? 3. The Need for a Managed Spot Market. 4. Open Electrical Energy Markets. 5. The Managed Spot Market. 6. The Settlement Process. 7. Further Reading. 8. Problems. 4. Participating in Markets for Electrical Energy. 1. Introduction. 2. The Consumer's Perspective. 3. The Producer's Perspective. 4. Perspective of Plants with Very Low Marginal Costs. 5. The Hybrid Participant's Perspective. 6. Further Reading. 7. Problems. 5. System Security and Ancillary Services. 1. Introduction. 2. Describing the needs. 3. Obtaining Ancillary Services. 4. Buying Ancillary Services. 5. Selling Ancillary Services. 6. Further Reading. 7. Problems. 6. Transmission Networks and Electricity Markets. 1. Introduction. 2. Decentralized Trading over a Transmission Network. 3. Centralized Trading over a Transmission Network. 4. Further Reading. 5. Problems. 7. Investing in Generation. 1. Introduction. 2. Generation Capacity from an Investor's Perspective. 3. Generation Capacity from a Customer's Perspective. 4. Further Reading. 5. Problems. 8. Investing in Transmission. 1. Introduction. 2. The Nature of the Transmission Business. 3. Cost--based Transmission Expansion. 4. Value--based Transmission Expansion. 5. Further Reading. 6. Problems. Appendix: Answers to Selected Problems. Abbreviations and Acronyms. Index.

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Fundamentals of power system economics

This tutorial paper discusses some aspects of electricity markets from the perspective of the demand-side. It argues that increasing the short-run price elasticity of the demand for electrical energy would improve the operation of these markets. It shows, however, that enhancing this elasticity is not an easy task. The tools that consumers and retailers of electrical energy need to participate more actively and effectively in electricity markets are discussed. The paper also describes how consumers of electricity can take part in the provision of power system security.

Demand-side view of electricity markets

This two-part paper surveys the frequency and voltage control ancillary services in power systems from various parts of the world. In this second part, essential economic features that must be taken into account when designing markets for ancillary services are first discussed. The methods adopted in eight different systems (Australia, France, Germany, Great Britain, New Zealand, PJM, Spain, and Sweden) for trading frequency and voltage control ancillary services are then compared. Lastly, new indicators for comparing volumes and costs of ancillary services across systems are proposed and calculated for the systems included in this survey. The companion paper surveys the technical features of these ancillary services

A Survey of Frequency and Voltage Control Ancillary Services—Part I: Technical Features

Spinning reserve (SR) allows system operators to compensate for unpredictable imbalances between load and generation caused by sudden outages of generating units, errors in load forecasting or unexpected deviations by generating units from their production schedules. As the proportion of power produced by wind farms increases, it becomes more difficult to predict accurately the total amount of power injected by all generators into the power system. This added uncertainty must be taken into account when setting the requirement for SR. This paper proposes a technique to calculate the optimal amount of SR that the system operator should provide to be able to respond not only to generation outages but also to errors in the forecasts for load and wind power production. Using a Monte Carlo simulation, the proposed technique for setting the SR requirements is then compared with the traditional deterministic criterion (i.e., the capacity of the largest online infeed), an approach to cope with wind imbalances and an approach that combines the traditional criterion with the approach to cope with wind imbalances. The results show that, contrary to what is commonly believed, an increased wind power penetration does not necessarily require larger amounts of SR.

Estimating the Spinning Reserve Requirements in Systems With Significant Wind Power Generation Penetration

Because of the introduction of competition in the electricity supply industry, it has become much more important to be able to determine which generators are supplying a particular load, how much use each generator is making of a transmission line and what is each generator's contribution to the system losses. This paper describes a technique for answering these questions which is not limited to incremental changes and which is applicable to both active and reactive power. Starting from a power flow solution, the technique first identifies the busses which are reached by power produced by each generator. Then it determines the sets of buses supplied by the same generators. Using proportionality assumption, it is then possible to calculate the contribution of each generator to the loads and flows. The applicability of the proposed technique is demonstrated using a 30-bus example.

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Daniel S. Kirschen

Papers

Fundamentals of power system economics

Demand-side view of electricity markets

A Survey of Frequency and Voltage Control Ancillary Services—Part I: Technical Features

Estimating the Spinning Reserve Requirements in Systems With Significant Wind Power Generation Penetration

Contributions of individual generators to loads and flows